Fuzzy mixed variational-like and integral inequalities for strongly preinvex fuzzy mappings

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dc.contributor.authorKhan, Muhammad Bilal
dc.contributor.authorSrivastava, H.M.
dc.contributor.authorMohammed, Pshtiwan Othman
dc.contributor.authorGuirao, Juan L. G.
dc.date.accessioned2022-11-13T15:22:21Z
dc.date.available2022-11-13T15:22:21Z
dc.date.copyright2021en_US
dc.date.issued2021
dc.description.abstractIt is a familiar fact that convex and non-convex fuzzy mappings play a critical role in the study of fuzzy optimization. Due to the behavior of its definition, the idea of convexity plays a significant role in the subject of inequalities. The concepts of convexity and symmetry have a tight connection. We may use whatever we learn from one to the other, thanks to the significant correlation that has developed between both in recent years. Our aim is to consider a new class of fuzzy mappings (FMs) known as strongly preinvex fuzzy mappings (strongly preinvex-FMs) on the invex set. These FMs are more general than convex fuzzy mappings (convex-FMs) and preinvex fuzzy mappings (preinvex-FMs), and when generalized differentiable (briefly, G-differentiable), strongly preinvex-FMs are strongly invex fuzzy mappings (strongly invex-FMs). Some new relationships among various concepts of strongly preinvex-FMs are established and verified with the support of some useful examples. We have also shown that optimality conditions of G-differentiable strongly preinvex-FMs and the fuzzy functional, which is the sum of G-differentiable preinvex-FMs and non G-differentiable strongly preinvex-FMs, can be distinguished by strongly fuzzy variational-like inequalities and strongly fuzzy mixed variational-like inequalities, respectively. In the end, we have established and verified a strong relationship between the Hermite–Hadamard inequality and strongly preinvex-FM. Several exceptional cases are also discussed. These inequalities are a very interesting outcome of our main results and appear to be new ones. The results in this research can be seen as refinements and improvements to previously published findings.en_US
dc.description.reviewstatusRevieweden_US
dc.description.scholarlevelFacultyen_US
dc.description.sponsorshipThis paper has been partially supported by Ministerio de Ciencia, Innovaci ón y Universidades, grant number PGC2018-097198-B-I00, and by Fundaci ón Séneca of Región de Murcia, grant number 20783/PI/18.en_US
dc.identifier.citationKhan, M. B., Srivastava, H. M., Mohammed, P. O., & Guirao, J. L. G. (2021). “Fuzzy mixed variational-like and integral inequalities for strongly preinvex fuzzy mappings.” Symmetry, 13(10), 1816. https://doi.org/10.3390/sym13101816en_US
dc.identifier.urihttps://doi.org/10.3390/sym13101816
dc.identifier.urihttp://hdl.handle.net/1828/14468
dc.language.isoenen_US
dc.publisherSymmetryen_US
dc.subjectpreinvex fuzzy mappings
dc.subjectstrongly preinvex fuzzy mappings
dc.subjectstrongly invex fuzzy mappings
dc.subjectstrongly fuzzy monotonicity
dc.subjectstrongly fuzzy mixed variational-like inequalities
dc.subject.departmentDepartment of Mathematics and Statistics
dc.titleFuzzy mixed variational-like and integral inequalities for strongly preinvex fuzzy mappingsen_US
dc.typeArticleen_US

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